Fig. 1.1 Snapshot of a swell. (Photo 14568824, dreamstime.com.)
We can learn a lot about ocean waves just by looking. So before we become immersed in the intricacies of waves, let’s just stroll along the shore and comment on what we see. It’s a nice, sunny day, without much wind: a perfect day for the beach.
As we look out to sea, we see a long train of parallel, equally spaced waves approaching the shore, as is shown in figure 1.1. These waves were probably generated by the winds of the storm that passed far offshore a couple of days ago. The sea is still recovering from the storm.
But what exactly are we looking at? The sea is not pouring steadily up the beach like a broad river. If it were, we’d be drowned. Instead, as each wave collapses on the beach, the water sloshes back into the sea. So we realize that these waves are part of a moving pattern of humps and hollows that glides over the surface of the sea. This regular pattern is called a swell. Swell waves are usually low, only about a meter high or so, and have rounded tops. All the crests we see are nearly parallel to the shore, have about the same height, and extend sideways at least six or seven times the distance between crests.
I’d guess that in this swell, the distance between the crest and the trough (which is called the “height” of the wave) is about 1 m. We could estimate the distance between wave crests (which is appropriately called the wavelength) as about 10m, or 33 feet. And if we timed the interval between crests as they pass that buoy out there, we’d find the “period”: about 5 seconds for these waves. Divide one number by the other and we get the speed of the wave, about 2 m/s, or 7km/h, or about 4mph—the pace of a fast walk.
There’s a swimmer out there, floating on her back. Notice how she rises and falls rhythmically as each wave passes her. Although the waves are moving toward shore, she hardly advances shoreward. Her motion follows that of the water beneath her. It may seem surprising, but the water in a wave doesn’t actually travel with the wave toward the shore; it just bobs up and down, practically in place. We’ll talk more about this oscillating motion, and lack of forward motion, later on.
If this swimmer were to dive below the surface, she’d discover that the oscillations of the water gradually become weaker and weaker the deeper she dives. A few meters below the surface she would float in practically still water. Submariners are familiar with this phenomenon; they can escape a violent storm at the surface by diving deep enough to reach calm water.
Back on our beach, we see some kids playing in the surf zone where the small waves finally break. One little guy ventures out too far and gets knocked over by a wave. He’s all right; he picks himself up and runs back up the beach. His little accident reminds us, however, that a breaking wave carries a punch. Or in more technical terms, a wave carries the energy the wind gave it and releases that energy when it breaks. When a wave breaks, its energy accelerates the water, which then has enough momentum to knock you over. If you’ve ever waded out through the surf to reach quiet water beyond the breaking waves, you’ll understand what I mean.
This beach that we’re walking along is curved in a deep arc, a C shape maybe 2km long. As we walk toward the rocky point at the far end, we keep a sharp eye on the waves offshore. We notice that everywhere along the beach, the waves come rolling in parallel to shoreline. Somehow the waves rolling in from the horizon turn so as to face the shore at every point. How is this possible? This effect is called refraction, and we’ll learn how it works later on. Every type of wave (such as sound, seismic, or electromagnetic) exhibits refraction.
As we walk along, we notice that the appearance of the breaking waves changes from place to place. Where we started out, the beach sloped very gently into the water and the waves broke very gently. These were “spilling” waves; you can see an example in figure 1.2 (top).
Fig. 1.2 Top, a spilling wave; bottom, a plunging wave. (Photos 12068479, 3918008, dreamstime.com.)
Further along, the beach becomes steeper, and the crest of each wave curls and plunges forward as it reaches the beach (the “plunging” waves in fig. 1.2, bottom). Avid surfers look for a beach with just the right amount of slope to create a good plunging breaker. Finally, we reach a part of the beach that slopes very steeply away from a cliff, and here the waves barely rise up before smashing against the cliff. These are called “surging” waves.
Later on we’ll examine this connection between the shape of breakers and the slope of the beach in more detail.
We pass two little girls who are dropping pebbles into a circular pool of water they’ve dug in the sand. As a pebble falls in the water, it creates a circular ripple that spreads out and reflects from the edge of the pool toward the center, as can be seen in figure 1.3A. This event is a small version of a tsunami! The pebble represents the undersea earthquake that launches a group of waves across the water. The waves cross the ocean and reflect back from a coast. This effect was seen in the Indonesian tsunami of 2004. It crossed the Pacific Ocean basin at 750km/h and bounced off the east coast of Africa. Incidentally, reflection is another universal property of waves.
Fig. 1.3 A, circular waves arise when we drop a pebble into a pool. When they reach a border they are reflected. B, the cross-hatched interference pattern that arises after dropping two pebbles at the same time.
Before we leave the girls playing by the pool, watch what happens when they drop two pebbles at the same time. Now we have two circular patterns that expand outward and cross each other, as shown in figure 1.3B. When two crests overlap, the result is a taller crest; when a crest and a trough overlap, they cancel each other and the result is a draw. This interference of water waves is remarkable: they can pass over and through each other without disruption, but only if the waves have small heights compared with their wavelengths. Tall, steep waves can behave quite differently, as we shall see later on. Once again, interference is a behavior common to all types of waves.
Let me digress from our stroll on the beach to note that interference patterns in the ocean have been used in a very practical application: navigation. The natives of Micronesia and Polynesia were famous for the long voyages they made in open canoes across hundreds and thousands of miles of empty ocean. They could be out of sight of land for many weeks, and yet they could locate a tiny island in the midst of the vast ocean.
To navigate they used a variety of aids, such as the stars, cloud formations, winds, currents, and the flight of birds. In addition, the natives of the Marshall Islands in the western Pacific developed a special skill. They learned to read the interference patterns of swells that were driven by the prevailing northeast trade winds. Swells bend around islands and spread out in the channels between them. The overlap of swells from different directions produces a distinctive interference pattern that can help to fix your location.
The Marshall Islanders preserved their knowledge of the sea in so-called stick charts, which were passed down through the generations. The charts were made of strips of coconut leaf midrib and wood. Small cowrie shells were attached to the framework to represent individual islands. Curved strips represented the zones where interference patterns could be found. Other strips represented currents. A skilled navigator would orient the chart with the sun or stars and look for a particular interference pattern to guide his voyage. A simple but effective scheme!
Now let’s climb to the top of the high cliff that looks down on the shore. From there we can see how a swell interacts with itself and with a small island offshore. In figure 1.4 a swell is traveling from the lower right to the upper left. As it brushes against the mainland, the right ends of its wave turn slightly (refract) to face the cliff (notice the little bends in the ends). Then these refracted waves reflect off the promontory and interfere with the oncoming waves.
We can also see a good example of diffraction as the swell squeezes between the island and the mainland: a series of spreading circular arcs. Finally we see another swell entering from the left and interfering with the diffracted waves. Once again, reflection, refraction, diffraction, and interference are basic processes that all types of waves exhibit. So not only ocean waves, but also sound waves, light waves, and seismic waves show them.
Ah, but now the wind is picking up. We’re about to see how the sea changes under a rising wind. At first we see small waves building on top of the existing swell. These ripples break up almost immediately into small whitecaps because of the force of the wind. This is what’s called a choppy sea, or a chop for short.
Fig. 1.4 Looking down on the sea from a cliff, we can see several phenomena common to all types of waves: reflection, refraction, interference, and diffraction.
Fig. 1.5 An example of a “sea,” a jumble of short, high, pointed crests. (Photo 19376143, dreamstime.com.)
Fig. 1.6 Types of waves, arranged by period. (LPG refers to long-period gravity waves.) The curve indicates the amount of energy each type possesses.
Now the wind is rising very quickly; we are having a fierce squall. After a short while the sea is churned into chaos, with tall waves running in directions away from the wind and breaking into whitecaps. Sailors would call this a “sea” (fig. 1.5). Finally, in a gale or hurricane the ocean becomes a “fully developed sea.” Now the wave crests have sharp pointed tops, are irregular in height, and extend sideways only a few wavelengths. Short waves are piled on top of long waves, and the sea surface is bouncing up and down erratically. A small boat could easily be swamped in such a sea.
This is a good place to summarize the basic properties of ripples, chop, seas, swells, tsunamis, tides, and other types of waves. In figure 1.6 we see these waves arranged in order of period. The curve indicates the amount of energy each type possesses in the sea.
Well, the wind has turned cold. We’ll meet all these waves again, along with some scientists who have studied them, but for now it’s time to move on.
